Help With Adding Bones To An Already Deformed Armature
Go into 'Edit Mode', Shift+a to add an armature bone. Parent the new bone to the existing armature. Place the bone within the mesh at the proper location. Even if the mesh model is already parented to the armature, parent the mesh again to the full new armature. 

In 'Edit Mode' the PoseBone deformations will not show. In 'Pose Mode' you can deform the armature and the mesh model will follow. 

If the automatic weight painting is not satisfying, you can manually edit the weight painting for each bone in the armature. You do this by clicking on the mesh, and then selecting 'Weight Paint'. Then select the armature that you want to fix the weight distribution.

Good Luck!